Okay, I admit it... I found myself wondering whether this was in fact a real robot, or actually a person pretending to be a robot or even a fake robot.

It's not a fake. This is the latest iteration of Geminoid series of ultra-realistic androids, from Kokoro and Hiroshi Ishiguro. Specifically, this is Geminoid DK, which was constructed to look exactly like Associate Professor Henrik Scharfe of Aalborg University in Denmark.
UPDATE: Wow. We've just found a new video that is a-b-s-o-l-u-t-e-l-y incredible: